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Solutions of a class of higher order variable coefficient homogeneous differential equations

文献类型：期刊论文

作者Xu, Tingting3; Deng, Linhua3; Shan, Yulin2; Wan, Miao3; Zhou, Weihong1,3
刊名NETWORKS AND HETEROGENEOUS MEDIA
出版日期2025
卷号20期号:1页码:213-231
关键词variable coefficient homogeneous differential equations linearly independent solutions rank of coefficient matrices fourth-order and nth-order equations
ISSN号1556-1801
DOI10.3934/nhm.2025011
文献子类Article
英文摘要Recently, the variable coefficient homogeneous differential equations (VCHDE) have been widely applied to real-world problems, such as wave propagation and material science. However the exploration and research on higher-order VCHDE is relatively lagging. Given this, this work focuses on the solutions of fourth-order and nth-order VCHDE with polynomial coefficients. By means of the sufficient conditions for the existence of solutions to differential equations, a connection is established between the rank of the variable coefficient matrix and the existence of polynomial particular solutions. The main results show that: (1) the necessary and sufficient conditions for the existence of polynomial particular solutions of fourth-order VCHDE are derived; (2) the necessary and sufficient conditions for the existence of only one polynomial particular solution, or the existence of two, three, or four linearly independent polynomial particular solutions of fourth-order VCHDE are proved; (3) the necessary and sufficient conditions for the existence of only one polynomial particular solution, or the existence of two, three, or four linearly independent polynomial particular solutions of nth-order VCHDE are proved. These results not only extend the class of solvable differential equations, but also provide a new way of thinking about the existence of solutions to VCHDE.
学科主题数学
URL标识查看原文
出版地PO BOX 2604, SPRINGFIELD, MO 65801-2604, UNITED STATES
WOS关键词EXISTENCE
资助项目National Nature Science Foundation of China[12463009]; Yunnan Fundamental Research Projects[202301AV070007]; Yunnan Fundamental Research Projects[202401AU070026]; Yunnan Fundamental Research Projects[202401AT070955]; Yunnan Fundamental Research Projects[202401AU070296]; The Yunnan Revitalization Talent Support Program Innovation Team Project[202405AS350012]; Scientific Research Foundation Project of Yunnan Education Department[2023J0624]; Scientific Research Foundation Project of Yunnan Education Department[2024Y469]; Scientific Research Foundation Project of Yunnan Education Department[2025Y0720]; Scientific Research Foundation Project of Yunnan Education Department[2025Y0721]; Scientific Research Foundation Project of Yunnan Education Department[2025J0502]; GHfund A[202407016295]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:001440277800001
出版者AMER INST MATHEMATICAL SCIENCES-AIMS
资助机构National Nature Science Foundation of China[12463009] ; Yunnan Fundamental Research Projects[202301AV070007, 202401AU070026, 202401AT070955, 202401AU070296] ; The Yunnan Revitalization Talent Support Program Innovation Team Project[202405AS350012] ; Scientific Research Foundation Project of Yunnan Education Department[2023J0624, 2024Y469, 2025Y0720, 2025Y0721, 2025J0502] ; GHfund A[202407016295]
版本出版稿
源URL[http://ir.ynao.ac.cn/handle/114a53/28195]  
专题云南天文台_中国科学院天体结构与演化重点实验室
作者单位1.Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming, Yunnan, 650011, China
2.School of Mathematics and Computer Science, Chuxiong Normal University, Chuxiong 675000, Yunnan, China;
3.School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650504, Yunnan, China;
推荐引用方式
GB/T 7714		 Xu, Tingting,Deng, Linhua,Shan, Yulin,et al. Solutions of a class of higher order variable coefficient homogeneous differential equations[J]. NETWORKS AND HETEROGENEOUS MEDIA,2025,20(1):213-231.
APA Xu, Tingting,Deng, Linhua,Shan, Yulin,Wan, Miao,&Zhou, Weihong.(2025).Solutions of a class of higher order variable coefficient homogeneous differential equations.NETWORKS AND HETEROGENEOUS MEDIA,20(1),213-231.
MLA Xu, Tingting,et al."Solutions of a class of higher order variable coefficient homogeneous differential equations".NETWORKS AND HETEROGENEOUS MEDIA 20.1(2025):213-231.

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来源：云南天文台

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